Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations.
y=x+3
−4x+4y=28
To begin, we will graph each equation separately.
For the equation y = x + 3, we can start by assigning arbitrary values to x and solving for the corresponding values of y. Let's use x = 0, 1, and 2:
If we let x = 0, then y = 0 + 3 = 3. So one point on the graph is (0, 3).
If we let x = 1, then y = 1 + 3 = 4. So another point on the graph is (1, 4).
If we let x = 2, then y = 2 + 3 = 5. So a third point on the graph is (2, 5).
Plotting these points on a graph and connecting them with a straight line, we get:
Next, let's graph the equation -4x + 4y = 28. We can rearrange this equation to solve for y:
4y = 4x + 28
y = x + 7
Using the same process as before, we can assign values to x and find the corresponding values of y. Let's use x = 0, 1, and 2 again:
If we let x = 0, then y = 0 + 7 = 7. So one point on the graph is (0, 7).
If we let x = 1, then y = 1 + 7 = 8. So another point on the graph is (1, 8).
If we let x = 2, then y = 2 + 7 = 9. So a third point on the graph is (2, 9).
Plotting these points on the same graph as the first equation, we get:
From the graph, we can observe that the two lines intersect at the point (4, 7). This point represents the solution to the system of linear equations. Therefore, the solution to the system is x = 4 and y = 7.